Mathematical foundations Books

This text unites logical and philosophical aspects of set theory in a manner intelligible to mathematicians without training in formal logic and to logicians without a mathematical background. 1961 edition.

These volumes present a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided deisgn (CAD) and computer graphics.

Together with its compagnion volume this book presents a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided design (CAD) and computer graphics.

Regression Analysis and Its Application: A Data-Oriented Approach answers the need for researchers and students who would like a better understanding of classical regression analysis. Useful either as a textbook or as a reference source, this book...

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential...

This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of...

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides...

This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the...

Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential...

This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of two or three dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution...

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of...

Techniques for Designing and Analyzing Algorithms Design and analysis of algorithms can be a difficult subject for students due to its sometimes-abstract nature and its use of a wide variety of mathematical tools. Here the author, an experienced and...

This book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many...

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he...

A radical and challenging book which argues that artificial intelligence needs a completely different set of foundations, based on ecological intelligence rather than human intelligence, if it is to deliver on the promise of a better world. This can...

This book tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental...

Soft computing techniques are no longer limited to the arena of computer science. The discipline has an exponentially growing demand in other branches of science and engineering and even into health and social science. This book contains theory and...

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, this book provides complete and rigorous...

First Published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that...

There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of...

IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised...

Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is...

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which...

Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents...

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific dis­ ciplines and a resurgence of interest in the modern as well as the classical...

Preface.- Background Material.- Simple economies-complete and incomplete markets.- Investment Portfolio Optimization.-Pricing: Neutral and Indifference.- Hedging.- Equity Valuation and Investing.- FX Rates and FX Derivatives.- Appendix.- References.-

This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on...

This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential...

Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers...

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra,...

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise"...

Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as...

This book presents fundamental concepts of optimization problems and its real-world applications in various fields. The core concepts of optimization, formulations and solution procedures of various real-world problems are provided in an easy-to-read...

Functional Linear Algebra is a unique text authored to address the need for a one-term linear algebra course when students have only had calculus. It does no assume students have had a proofs course.

This book focuses on cutting-edge innovations and core theories, principles, and algorithms applicable to a wide area. Real-life applications, case studies, and examples are included along with emerging trends, design, and optimized solutions pivoting...

The book differs from most texts on the topic by blending the use of computer simulations with inquiry-based learning (IBL). Students can discover examples and counterexamples through manipulations built into the software though a link to the website.

The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.

Classic study discusses number sequence and number language, then explores written numerals and computations in a wide range of cultures. 282 illustrations. "Superior narrative ability." - Library Journal.

The GUHA is a method of mechanizing hypothesis formation. The input of the GUHA procedure consists of analysed data and several parameters defining a large set of relevant patterns. The output is a representation of a set of all relevant patterns...

This book offers a constructive approach to the inner product space formulation of Quantum Mechanics as opposed to inductive approaches based on intuitive associations or blatant axiomatic approaches. It strives to explain the purpose and meaning of the...